Problem 5-7 An FAA engineer has collected the following aircraft-landing-acciden

Question

Problem 5-7 An FAA engineer has collected the following aircraft-landing-accident data Number of Crashes Nearest Distance from Runway (feet 32 15 100 200 1000 2000 5000 The Table below is better for pasting into Splus or MATLAB. NC (Y) NDFR (X) 32 100 15 200 6 1000 2 2000 1 5000 Lapin says to determine the logarithmic regression line using distance as the independent variable. Translated that means fit log Y = X when I plotted log(Y) versus X, the data didn't look linear. So instead fit log(Y) versus log(X). Note: log = natural logarithm. This is Splus and MATLAB convention. Howeve intercept of the log-log regression line= 745130 slope of the log-log regression line= 0.86847 Suppose that the nearest distance is 125. Estimate the average number of crashes at that distance (don't forget to use log of the distance and then exponentiate--exp(t)) 3.258

Explanation / Answer

calculation procedure for regression
mean of X = X / n = 11.2
mean of Y = Y / n = 1660
(Xi - Mean)^2 = 662.8
(Yi - Mean)^2 = 16272000
(Xi-Mean)*(Yi-Mean) = -71760
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
= -71760 / 662.8
= -108.26795
bo =   Y / n - b1 * X / n
bo = 1660 - -108.26795*11.2 = 2872.60109
value of regression equation is, Y = bo + b1 X
Y'=2872.60109-108.26795* X

125 = 2872.60109-108.26795* X
108.26795* X = 2872.60109 - 125
x = 2747.60109/108.26795
x = 25.377
Avegrage no.of crashes at 125 distance is 25.377 ~ 26  

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 32 100 432.64 2433600 -32448 15 200 14.44 2131600 -5548 6 1000 27.04 435600 3432 2 2000 84.64 115600 -3128 1 5000 104.04 11155600 -34068

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